Question

divide

p(x) = 3x⁴+4x³+4x²+8x-1 by
q(x)= 3x+1
also find what should be added to px to divide completely by qx ​

Answer 1

Step-by-step explanation:

3x

3

−x

2

−x−4

__________________

x−1)3x

4

−4x

3

+0x

2

−3x−1

3x

4

−3x

3

__________________

−x

3

+0x

2

−3x

−x

3

+x

2

________________

−x

2

−3x−1

−x

2

+x

_______________

−4x−1

−4x+4

_______________

−5

∴

x−1

3x

4

−4x

3

−3x−1

=3x

3

−x

2

−x−4

Remainder=−5

Now to check whether x+1 is factor or not,

x+1=0

x=−1

Put x=−1 in 3x

4

−4x

3

−3x−1

3(−1)

4

−4(−1)

3

−3(−1)−1

=3+4+3−1

=9



=0

∴ By Remainder theorem, we conclude (x+1) is not a factor.